Engineering Structures 175 (2018) 86–100 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Wind-induced responses of tall buildings under combined aerodynamic control T ⁎ Chaorong Zhenga,b, , Yu Xieb, Mahram Khanb, Yue Wua,b, Jing Liuc,d a Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China c Heilongjiang Provincial Key Laboratory of Building Energy Eﬃciency and Utilization, Harbin 150090, China d School of Architecture, Harbin Institute of Technology, Harbin 150090, China b A R T I C LE I N FO A B S T R A C T Keywords: Tall building Wind-induced response Combined aerodynamic control Shape optimization Air suction The new trend towards constructing taller buildings makes modern tall buildings be increasingly susceptible to wind excitations. Therefore, a combined aerodynamic control, including the shape optimization of the crosssection (passive aerodynamic control) and air suction (active aerodynamic control), is put forward to achieve a more considerable reduction of the wind-induced responses of a tall building with square cross-section, so as to improve its wind-resistance performance. Firstly, based on the wind excitations acquired by wind tunnel test of four suction controlled tall building models with diﬀerent cross-sections (consists of the square, corner-recessed square, corner-chamfered square and Y-shaped cross-sections, and are denoted as Models 1–4 respectively), the wind-induced responses of the prototype tall buildings and simpliﬁed mass-spring models are calculated using the time history analysis method. Secondly, eﬀects of the suction ﬂux coeﬃcient CQ, shapes of the cross-sections and wind direction angles θ on the characteristics of the wind-induced responses are analyzed. The results show that the combined aerodynamic control is very eﬀective in reducing the along-wind and across-wind responses at most cases, however, it can sometimes be unfavorable to the torsional responses. Among the four tall buildings, Model 2 has the best performance in the along-wind direction, with a maximum reduction of the extremum tip displacement of 34% caused by the shape optimization, and 29% caused by the air suction and a total of 63% caused by the combined aerodynamic control at a relatively low CQ (CQ = 0.0159). However, the regularity is quite diﬀerent for the across-wind responses; when θ is equal to 0°, the maximum reduction of the extremum tip displacement in the across-wind direction caused by the shape optimization and air suction are 49% for Model 4 and 47% for Model 1 respectively. Finally, a quantitative discussion on the reduction of the wind-induced responses of tall buildings caused by the combined aerodynamic control is conducted, which can provide a valuable reference for further studies or potential engineering applications. 1. Introduction During the past decades, with the advances in high-strength and light-weight structural materials, and new generation of structural systems and construction technologies, tall buildings with increased height and complicated shape have been continuously built up. Generally, tall buildings of this kind have reduced structural mass, stiﬀness, and damping ratio. And hence, they are usually very susceptible to wind excitations, which have the potential to reduce their structural safety or cause discomfort to the occupants [1–3]. Therefore, how to reduce the wind loads and wind-induced responses, so as to ensure acceptable performance for survivability, serviceability and habitability, is of great concern for the researchers and engineers in wind engineering. According to the vibration control theory, there are mainly three kinds of measures adopted to mitigate the wind-induced responses [4,5]: (1) Structural measures: Recent development of advanced structural systems, such as bundled tubes, belt trusses, outrigger trusses, vierendeel-type bandages and mega frame systems etc., signiﬁcantly increase the structural mass, stiﬀness and natural frequency of tall buildings [5,6]. (2) Damping measures: Incorporation of auxiliary damping devices ⁎ Corresponding author at: Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China. E-mail address: ﬂyﬂuid@163.com (C. Zheng). https://doi.org/10.1016/j.engstruct.2018.08.031 Received 15 January 2018; Received in revised form 13 July 2018; Accepted 11 August 2018 0141-0296/ © 2018 Elsevier Ltd. All rights reserved. Engineering Structures 175 (2018) 86–100 C. Zheng et al. changes in its cross-section. In some cases, the change in cross-section over the building height can be achieved through smoother modiﬁcations by twisting movements (as for example in the case of Shanghai Tower, completed in 2016, which is twisted by 120°, shown in Fig. 1c). Despite the enormous advantages that can be acquired by the passive aerodynamics control, inherent limitations make the aerodynamic shape tailoring not always suﬃcient to reach the desired response level. Generally, the aerodynamic shape tailoring can only reduce the drag force and base moment less than 25% [16], and the reduction of the tip displacement and acceleration are usually less than 30% and 15% respectively [17]. In order to improve the robustness of the passive aerodynamic control and to further reduce the wind loads and wind-induced responses, several active aerodynamic control measures, such as the oscillating surface [18], moving surface boundary-layer control (MSBC) [19], aerodynamic ﬂap system [20,21], traveling wave wall [22], and air suction or blowing [23–26] etc. to generate virtual modiﬁcation of building shapes, were proposed. Suction control, which was ﬁrst utilized by Prandtl [27] to control the ﬂow separation of a circular cylinder, has been proved to be a very eﬀective means to control the vortex shedding for numerous ﬂow conﬁgurations, such as the airfoil ﬂows [24,28], the compressor cascade ﬂows and the backward-facing step ﬂows [23,29], and to improve the wind-resistance performance for high-rise buildings [25,26] and bridges [30]. The basic principle of suction control is to restrain the ﬂow separation and vortex shedding of a bluﬀ body by absorbing the low-speed ﬂows in the boundary layer [31,32], resulting in a signiﬁcant reduction of aerodynamic forces. In our previous work, CFD simulation [26], wind tunnel test [33], and PIV (Particle Image Velocimetry) experiment [34] were conducted to systematically investigate the characteristics of wind loads of tall buildings controlled by air suction and to explore the mechanism of suction control. However, a more promising trend is to combine the passive and active aerodynamic control, so as to achieve a more considerable control eﬀect over the wind loads and wind-induced responses, and also avoid their individual disadvantages (such as the inherent limitations of the passive aerodynamic control and large energy input for the active aerodynamic control). Therefore, in the present paper, a combined aerodynamic control (consists of the shape optimization of the cross-section and air suction) are put forward to reduce the wind-induced responses of a tall building. And eﬀects of the suction ﬂux [7–9], including the passive dampers (such as the steel damper, viscous damper, Tuned Mass Dampers (TMD), Tuned Liquid Dampers (TLD), etc.) and active dampers (such as the Active Mass Dampers (AMD), Hybrid Mass Dampers (HMD), Active Variable Stiﬀness (AVS), etc.), into tall buildings to enhance their capacity of dissipating energy. (3) Aerodynamic measures: Improving the aerodynamic performance of tall buildings via passive aerodynamic control or active aerodynamic control to reduce wind excitations. The passive aerodynamic control, such as implementing shape optimization of the cross-section [10–12], modiﬁcations of the cross-section along the height [13,14], and vertical or horizontal through building openings [10] etc. to generate the aerodynamic shape tailoring, is a powerful means to achieve optimal wind-resistance performance for tall buildings [15]. Modiﬁcations of the cross-sectional shape, as for example the inclusion of recessed corners, chamfered corners, horizontal slotted corners and Y shape [1,11], have been found to considerably reduce the wind loads and wind-induced responses of tall buildings, in comparison to those of a basic square cross-sectional tall building. As for the longitudinal modiﬁcations, the inclusion of setback, tapering and helical shapes, the progressive elimination of corners or rotation of cross-section with the height not only are characteristics of some of the most graceful and notable buildings, but also have been demonstrated to have a practical aerodynamic purpose [13,14]. Some recent examples have shown that the passive aerodynamic measures that create aerodynamically eﬃcient forms can be integrated into the design of tall buildings without sacriﬁcing their appearance. For example, in the case of the Taipei 101 Tower, completed in 2004 (Fig. 1a), every group of eight ﬂoors constitutes a tapered segment, creating a pattern that recalls important cultural symbolism and enhancing at the same time the aerodynamic performance [3]. As is illustrated by Irwin [16], the double recessed corners can generate a 25% reduction of base moment for the Taipei 101 Tower. More recent structure with setbacks along the height is the Burj Khalifa Tower, completed in 2010 (Fig. 1b) with a height of 828 m, which holds the record of the tallest building in the world. In particular, in this case, the inﬂuence of vortex-induced excitations was minimized by deterring the formation of a coherent wake structure, through frequent and drastic Fig. 1. (a) Taipei 101 Tower, (b) Burj Khalifa Tower, (c) Shanghai Tower. 87 Engineering Structures 175 (2018) 86–100 C. Zheng et al. is deﬁned as 0° when the wind direction is perpendicular to the windward face. coeﬃcient, diﬀerent cross-sections and wind direction angles on the wind-induced responses are analyzed to quantitatively discuss the reduction of the responses generated by the passive, active and combined aerodynamic control respectively. Section 2 is mainly concerned on setup of the wind tunnel test for a tall building model controlled by the combined aerodynamic measures, and Section 3 presents the time history analysis method to calculate the wind-induced responses of tall buildings. Characteristics of the wind-induced responses of the tall buildings in the along-wind, across-wind and torsional directions are analyzed in Section 4. And Sections 5 and 6 show discussions and the main conclusions. 2.2. Suction control system As is shown in Fig. 4, the suction control system mainly consists of three parts: two internal suction pipes inside the test model (see Fig. 4b), pump system (includes a pair of vortex fans, ﬂowmeters and ﬂow control valves) and external connections (includes the steel wire reinforced hoses and PVC pipes). Each internal suction pipe, which envelopes the suction air through the suction hole, is linked to the steel wire reinforced hose and then connected to the pump system. According to our previous research [26,39], the suction ﬂux coefﬁcient CQ, which is deﬁned by Eq. (1), is the most important parameter to dominate the suction control eﬀect. 2. Wind tunnel test setup The wind tunnel test is carried out in the Joint Laboratory of Wind Tunnel and Wave Flume located at Harbin Institute of Technology, China. The dimensions of the small test section are 25.0 m in length, 4.0 m in width and 3.0 m in height. A digital pressure measurement system DSM 3400 (SCANIVALVE Corp., America) is used to synchronously measure the multi-point pressures on scaled models with a sampling frequency of 625 Hz, and the total time of each measurement is 60 s. Three one-dimensional hot wires (DANTEC Corp., Denmark) are used to measure the wind speed. CQ = ρc Qc/(ρ∞ Q∞) = ρc dUc h/(ρ∞ D′UH H ) (1) where ρc and ρ∞ are the density of the suction air and the oncoming air (ρc = ρ∞ = 1.225 kg/m3) respectively; Qc and Q∞ are the ﬂux of the air suction through one suction hole and the oncoming air respectively; while Uc and UH are the suction speed normal to the side face and the oncoming wind speed at top of the test models, and UH is set as 7 m/s in this paper. Therefore, the Reynolds numbers based on maximum projecting width of each model and the top wind speed are about 8.07 × 104, 7.39 × 104, and 8.50 × 105 for Model 1, Models 2–3, and Model 4 respectively. The suction speed Uc and corresponding CQ for diﬀerent test models are listed in Table 1. 2.1. Test models Four tall building models, including a square model, corner-recessed square model, corner-chamfered square model and Y-shaped model (abbreviated as Models 1–4 respectively, and Model 1 is deﬁned as the baseline model), are adopted as the test models. The scaled models have a same height of 600 mm (H = 600 mm) but diﬀerent shapes of the cross-section. The geometric scale ratio of the scaled models is set as 1:300, so the height of the prototype tall building is 180 m. The corner recession/chamfering ratio of Models 2–3 are determined to be 10%, because these models have the best wind-resistance performance compared to other corner recession/chamfering ratios (such as 5% and 15%) based on our CFD simulations [33], and the results agree well with Zhang et al.’s experimental results [35] and other previous results [11,16,36]. Dimensions of the four cross-sections, which are designed to have a same usable ﬂoor area according to Tse et al.’s suggestion [37], are also shown in Fig. 2. It can be seen that the windward face widths (D) for Model 1, Models 2–3, and Model 4 are 118 mm, 120 mm, and 62 mm respectively, and the maximum transverse width (D′) for Model 4 is 177 mm, so the blockage ratio of the wind tunnel is less than 5%. To measure wind pressure around surfaces of the test models, there are 16, 26, 22 and 27 pressure taps distributed on the cross-sections of Models 1–4 with ten height levels, so the total number of pressure taps are 160, 260, 220 and 270 respectively. More detailed information about the arrangement of pressure taps on the test models can be found in Zhang’s thesis [38]. The dimensions of each suction hole, which is symmetrically located at each side face of the model with a distance of 10%D to its leading separation edge (see Figs. 2 and 3), is 400 mm in height (from the height 200 mm to 600 mm in Fig. 2, h = 400 mm) and 5 mm in width (d = 5 mm). Location of the suction holes (i.e. 10%D) is determined based on the comprehensive consideration of two aspects: Firstly, according to our previous research [26,39]), the control eﬀect will be better if the suction hole is closer to the leading separation edge; secondly, the distance between the suction hole and the leading separation edge should be long enough so that it is feasible to fabricate the internal suction pipes inside the test model. Fig. 3 shows the schematic diagram of the suction control on the square cross-section and deﬁnition of the wind direction angle. It can be seen that the suction angle is deﬁned as 90° when the direction of air suction is perpendicular to the side face, and the wind direction angle θ 2.3. Wind ﬁeld simulation The terrain roughness at the building site is assumed to be the exposure category C in the Chinese load code GB 50009-2012 [40], and the mean wind speed proﬁle and turbulence intensity proﬁle below the gradient wind height (zG = 450 m) can be expressed as U (z ) = UH (z / H )0.22 (2) Iu (z ) = I10 (SL·z /10)−0.22 (3) where UH is the reference wind speed at top of the test models, z is the height above ground of the wind tunnel, SL equals to 300 is the reciprocal value of the geometric scale ratio between the scaled model and the prototype tall building (see Section 3.2), and I10 is the turbulent intensity at a height of 10 m, set as 0.23 for the exposure category C. The passive devices, including the roughness elements, spires, a serrated barrier and a carpet (More detailed information can be found in Zhang [38]), are used to simulate the wind ﬁeld in the wind tunnel. 3. Wind-induced responses analysis method 3.1. Newmark method Analysis of wind-induced responses of a tall building is to solve the motion equilibrium equation (Eq. (4)) of the structure. mu¨ (t ) + cu̇ (t ) + ku (t ) = p (t ) (4) where m, c and k are the mass, damping constant and stiﬀness of the structure respectively, u (t ), u̇ (t ) and u¨ (t ) are the displacement, velocity and acceleration of the structure respectively, and p(t) is the wind excitation. Newmark method is a time-stepping method to solve the motion equilibrium equation using Eqs. (5) and (6). u̇i + 1 = ui + [(1−γ )Δt ] u¨ i + (γ Δt ) u¨ i + 1 ui + 1 = ui + (Δt ) u̇i + [(0.5−β )(Δt )2] u¨ (5) i + [β (Δt )2] u¨ i+1 (6) where ui (ui + 1), u̇i (u̇i + 1) and üi (üi + 1) are the displacement, velocity, and 88 Engineering Structures 175 (2018) 86–100 C. Zheng et al. Fig. 2. Dimensions (Unit: mm) and schematic diagrams of the test models: (a) square model, (b) corner-recessed square model, (c) corner-chamfered square model, (d) tapered model, and (e) Y-shaped model. Table 1 Arrangement of test cases. Test model Uc (m/s) CQ θ (°) Square model 0, 6, 0, 0, 6, 0, 0, 6, 0, 0, 6, 0, 0, 0.0081, 0.0161, 0.0203, 0.0242, 0.0323, 0.0365 0, 0.0242, 0.0365 0, 0.0079, 0.0159, 0.0198, 0.0238, 0.0317, 0.0356 0, 0.0238, 0.0356 0, 0.0079, 0.0159, 0.0198, 0.0238, 0.0317, 0.0356 0, 0.0238, 0.0356 0, 0.0054, 0.0108, 0.0135, 0.0162, 0.0216, 0.0243 0, 0.0162, 0.0243 0 Corner-recessed square model Corner-chamfered square model Y-shaped model 2, 8, 6, 2, 8, 6, 2, 8, 6, 2, 8, 6, 4, 9 9 4, 9 9 4, 9 9 4, 9 9 5, 5, 5, 5, Fig. 3. Schematic diagram of the suction control and wind direction angle. Fig. 4. Suction control system: (a) pump system and external connections, (b) internal suction pipes. 89 15, 30, 45 0 15, 30, 45 0 15, 30, 45 0 15, 30, 45, 60 Engineering Structures 175 (2018) 86–100 C. Zheng et al. 2.0x106 Start 1.5x106 1 β Δt 2 Fxj (N) Input the force P(t); time step t ; structure information [K], [M], [C]; value of , a = 0 Level 3 Level 7 1 γ ,a = ,a = 1 βΔt 2 βΔt 1.0x106 5.0x105 1 Δt γ γ a = - 1, a = - 1, , a = ( - 2) 3 2β 4 β 5 2 β 0.0 0 200 400 600 800 t (s) γ kˆ = k + m+ c β Δt β Δt 2 1 1.5x106 Ri +1 = Pi +1 + m(a0ui + a2ui + a3ui ) + c (a1ui + a4ui + a5ui ) 1.0x10 Displacement at time step i+1 5.0x105 Level 3 Level 7 Fyj (N) 6 ˆ Ku i +1 = Ri +1 0.0 -5.0x105 Acceleration and velocity at time step i+1 1 1 1 ui +1 = u + (1(u -u ))ui βΔt 2 i +1 i βΔt i 2β γ γ γ ui +1 = (1- )ui + (ui +1 -ui ) + (1)ui Δt 2β β β Δt -1.0x106 -1.5x106 0 200 400 600 800 t (s) i<n Level 3 Level 7 6.0x106 u u u Mzj (N·m) Output 9.0x106 End Fig. 5. Flow chart of the Newmark method. 3.0x106 0.0 -3.0x106 acceleration at time step i (i+1) respectively, Δt is the interval of every time step, the factors β and γ deﬁne the variation of acceleration over a time step and determine the stability and accuracy characteristics of the method. In the present paper, the constant average acceleration method is used, and the value of β and γ are determined to be 1/2 and 1/4 respectively. The ﬂow chart of the Newmark method is shown in Fig. 5. -6.0x106 -9.0x106 0 200 400 t (s) 600 800 Fig. 6. Time history of wind excitations of the square tall building. 3.2. Determination of wind excitation sampling frequency is 625 Hz in the wind tunnel test, the time step for the wind-induced response analysis can be determined to be 0.0776 s, and the total time is 12.93 min after 10,000 time steps of calculation. The time history of wind excitations at j story of each simpliﬁed mass-spring model (see Section 3.4) can be calculated by Eqs. (7)–(9), and the along-wind, across-wind and torsional wind excitations on two selected stories of the square tall building (Model 1) are shown in Fig. 6. According to GB 50009-2012 [40], the basic wind pressure (deﬁned in the exposure category B) in Harbin city of China is 0.55 kN/m2. So the oncoming wind speed at top of the tall building (180 m) in the exposure category C can be determined to be 43.35 m/s. Therefore, the wind speed ratio between the scaled model and the prototype building Um/Up is 7/43.35 equal to 1/6.19. Assume the geometric scale ratio between the scaled model and prototype tall building Bm/Bp is 1/300, so the frequency ratio fm/fp can be determined to be 48.47. As the 90 Engineering Structures 175 (2018) 86–100 C. Zheng et al. Fig. 7. FEM of the prototype tall building: (a) plan and (b) elevation. Fxj (t ) = 1 ρ UH2 hj B xj CFxj (t ) 2 ∞ (7) Fyj (t ) = 1 ρ UH2 hj B yj CFyj (t ) 2 ∞ (8) Mzj (t ) = 1 ρ UH2 hj B xj B yj CMzj (t ) 2 ∞ building, its damping ratio is 0.02 for all modes. Fig. 8 shows the ﬁrst 6 orders of natural frequency and modal shape of the prototype tall building. It can be seen that Modes 1 & 2 and Modes 4 & 5 are the vibrations in the lateral directions with a natural frequency of 0.218 Hz and 0.697 Hz respectively; and Mode 3 and Mode 6 are the vibrations in the rotational direction with a natural frequency of 0.293 Hz and 0.849 Hz respectively. (9) where Fxj(t), Fyj(t), and Mzj(t) are the wind forces in the x and y directions, and the torsional moment around the z direction respectively; hj is set as the height of the j story; Bxj and Byj are the transverse width normal to the x and y directions at the j story; CFxj(t), CFyj(t) and CMzj(t) are time history of the force coeﬃcient in the x and y directions, and the torsional moment coeﬃcient at the j story of each prototype tall building or simpliﬁed mass-spring model. 3.4. Simpliﬁed mass-spring model As the time history analysis of wind-induced responses for the prototype tall building is quite time consuming, a simpliﬁed massspring model is introduced to improve the computational eﬃciency but with enough accuracy. As is shown in Fig. 9, the prototype tall building used in Section 3.3 is simpliﬁed as a 10-story model with lumped masses and springs using ANSYS 14.0, in which every 6-story of the tall building are condensed into a point with mass (mi) and torsional moment of inertia (Ii), and a link with two lateral springs in x and y directions (whose stiﬀness is kx and ky respectively), a torsional spring (whose stiﬀness is kz) and a damper (whose damping constant is c). The mass and the torsional moment of inertia are modeled by a MASS21 element, and the lateral springs, torsional springs and dampers are modeled by a COMBIN14 element. The total mass of the simpliﬁed mass-spring model is 135432 t, which is very close to that of the prototype tall building (135322 t). The comparison of the ﬁrst 6 orders of natural frequency between the prototype tall building and the simpliﬁed mass-spring model is listed in Table 3, it can be seen that the deviations for the ﬁrst 3 orders of frequency are all 0. Fig. 10 compares the ﬁrst 3 orders of standardized modal shapes between the prototype building and the model, and a good agreement is found for the lateral and torsional modal shapes, 3.3. Prototype tall building As is shown in Fig. 7, the ﬁnite element model (FEM) of a steel braced frame structure with 60 stories and 6 bays in the plan is constructed using ANSYS 14.0, to simulate the prototype tall building with square cross-section (corresponds to Model 1). Dimensions of each story are 35.4 × 35.4 × 3 m3 with a uniform bay spacing of 5.9 m, so the total height of the tall building is 180 m. The steel braced frame structure consists of steel beams, ordinary steel columns and reinforced steel columns, chevron concentrically steel braces and steel slabs, and dimensions of these components are listed in Table 2. It can be seen that the columns have a box cross-section, and the beams and braces have an I-shaped cross-section. The columns and beams are modeled using the Beam188 Element, and the braces and slabs are modeled using the Link180 and Shell63 Elements respectively. The modulus of elasticity of steel is 210 GPa, and its yielding stress is 235 MPa. For the steel tall Table 2 Dimensions of the components of the prototype tall building (Unit: mm). Stories Ordinary columns (Beam188) Reinforced columns (Beam188) Beams (Beam188) Braces (Link180) Slabs (Shell63) 1-20 21-40 41-60 □1000 × 1000 × 50 □900 × 900 × 40 □600 × 600 × 35 □1500 × 1500 × 60 □1100 × 1100 × 50 □700 × 700 × 40 I700 × 300 × 12 × 30 I700 × 300 × 12 × 30 I700 × 300 × 12 × 30 I300 × 400 × 10 × 20 I300 × 400 × 10 × 20 I300 × 400 × 10 × 20 5900 × 5900 × 200 5900 × 5900 × 200 5900 × 5900 × 200 91 Engineering Structures 175 (2018) 86–100 C. Zheng et al. Fig. 8. The ﬁrst 6 modes of the prototype tall building: (a) Modes 1 & 2 with a frequency of 0.218 Hz, (b) Mode 3 with a frequency of 0.293 Hz, (c) Modes 4 & 5 with a frequency of 0.697 Hz, (d) Mode 6 with a frequency of 0.849 Hz. especially for the 3rd mode (the torsional mode). Considering the contributions to the structural wind-induced responses caused by the ﬁrst 3 modes are dominant, so it can be concluded that the simpliﬁed mass-spring model can accurately simulate the dynamic properties of the prototype tall building. Besides the dynamic properties, the extremum tip displacements in the lateral and torsional directions of the simpliﬁed mass-spring model under a wind direction angle of 0° are also compared with those of the prototype tall building (Model 1) in Fig. 11. The extremum displacement ue can be calculated by Eq. (10). ue = u + sign (u ) × g × σu Table 3 Comparison of natural frequency between prototype tall building and simpliﬁed mass-spring model. Mode Freq. of prototype tall building (Hz) Freq. of simpliﬁed massspring building (Hz) Deviation/% 1 2 3 4 5 6 0.218 0.218 0.293 0.697 0.697 0.849 0.218 0.218 0.293 0.580 0.580 0.839 0% 0% 0% 16.8% 16.8% 1.2% (10) increases, the trend of the extremum tip displacements of the two models is the same, and their values are close to each other, with a maximum deviation of 5.8%, 4.8% and 17% for the along-wind, acrosswind and torsional displacements respectively. However, the where u and σu are the mean displacement and root mean square (RMS) of displacement respectively, g is the peak factor as set as 2.5 in this paper, and sign() is the sign function. It can be seen in Fig. 11 that, as the suction ﬂux coeﬃcient CQ Fig. 9. Schematic diagram of the mass-spring model. 92 Engineering Structures 175 (2018) 86–100 C. Zheng et al. Standardized height (z/H) 1.0 the Y-shaped tall building), with a proportion of 34% and 30% respectively. The results are quite close to Kwok et al.’s research on the maximum reduction of along-wind tip displacement of the CAARC tall building (40%) caused by chamfered corners [41], and are slightly larger than Elshaer et al.’s study on the maximum reduction of the along-wind responses (29%) of a 120 m tall building generated by the aerodynamic optimization for corner modiﬁcations [12]. The above comparisons indicate that the experimental and analysis results of the tall building controlled by shape optimization of the cross-section in the present paper are within expected results. As CQ increases, the extremum tip displacement of Model 1 in Fig. 12a ﬁrst decreases slightly and then increases signiﬁcantly under a relative low CQ (e.g. CQ ≤ 0.0161), and then decreases gradually under larger CQ (e.g. CQ ≥ 0.0203). And the reason can be attributed to the ﬂow ﬁeld caused by the suction control [34], which can be expressed as follows: Firstly, suction control removes low-speed ﬂows in the boundary layer and deﬂects ﬂows towards the side faces, so the width of the recirculation region will be reduced, resulting in a reduction of the drag force and the corresponding along-wind displacement. Secondly, the length of the recirculation region will also be reduced due to the suction control, so the negative pressure on the leeward face will be enlarged, resulting in an increased drag force and along-wind displacement. Maybe the second aspect is dominant for Model 1 under a low CQ, while the ﬁrst aspect tends to take over under a large CQ. The maximum reduction of the extremum tip displacement of Model 1, which is caused by the suction control, can reach to 22% when CQ equals to 0.0365. As for Models 2–3, their extremum tip displacements show a trend in reduction when CQ increases, while it is not varied for Model 4. The maximum reduction of the tip displacement of Models 2–3 caused by the suction control can reach to 29% and 27% respectively when CQ equals to 0.0356. Therefore, the maximum total reduction of the tip displacement for Models 2–3, which is caused by the combined aerodynamic control, can reach to 63% and 51% respectively, indicating that the eﬀect of the combined aerodynamic control is very signiﬁcant. The along-wind RMS tip accelerations in Fig. 12b have the same trend with those of the extremum tip displacements in Fig. 12a. The maximum reduction of the RMS tip acceleration caused by combined aerodynamic control also belongs to Model 2, with a proportion of 58% (28% caused by shape optimization and 30% caused by air suction respectively). Based on the above statements, it can be concluded that the reduction of the along-wind extremum displacement and RMS tip acceleration (63% and 58% for Model 2) caused by the combined aerodynamic control in the present paper are signiﬁcantly larger than those acquired by some previous researchers, such as a reduction of the along-wind extremum displacement and RMS tip acceleration up to 43% and 51% for a 400 m super-tall building caused by using a new combined structural system [42], and 39% and 49% caused by using a 1000 t TMD [42]; and a reduction of the RMS tip acceleration up to 30% for the Shanghai World Financial Center (492 m) by using two TMDs with a total mass of 253 t [43], and about 28% for a 180 m tall building by using a pair of TLDs [44]. The above comparisons can in some extent indicate the eﬀectiveness of the combined aerodynamic control to mitigate the along-wind responses of tall buildings. The along-wind extremum tip displacements of Models 1–4 at different wind direction angles θ are shown in Fig. 13. When there is no suction control (see Fig. 13a), the extremum tip displacement of Model 1 shows a slight decrease as θ increases, and the maximum value occurs when θ equals to 0°. However, for other models, the extremum tip displacement shows a sharp increase as θ increases, and the maximum value occurs when θ equals to 30° for Models 2 & 4 and 45° for Model 3. Furthermore, the shape optimization can reduce the tip displacements when θ is less than or equal to 30°, and among them Model 4 has the best wind-resistance performance. When there is suction control (see Fig. 13b), the above regularities are also observed for these Models Modes 1 & 2 - prototype Modes 1 & 2 - model Mode 3 - prototype Mode 3 - model 0.8 0.6 0.4 0.2 0.0 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Standardized modal shape Along-wind displacement - model Along-wind displacement - prototype Across-wind displacement - model Across-wind displacement - prototype 140 3.0x10-3 2.5x10-3 120 2.0x10-3 100 1.5x10-3 80 Torsional displacement - model Torsional displacement - prototype 1.0x10-3 60 0.00 0.01 0.02 0.03 Extremum tip torsional displacement (rad) Extremum tip displacement (mm) Fig. 10. Comparison of standardized modal shapes for prototype tall building and simpliﬁed mass-spring model. 0.04 CQ Fig. 11. Comparison of the extremum tip displacements between the simpliﬁed mass-spring model and prototype tall building. computational eﬃciency for the time history analysis has been much improved by using the simpliﬁed mass-spring model, as its computational time for 10,000 time steps is about 1 h, which is much less than 12 h of the prototype tall building. It should be noted that, it is the aim to investigate the eﬀect of the combined aerodynamic control on the wind-induced responses of tall buildings in the present paper, so the dynamic properties of the four tall buildings (i.e. the prototype tall buildings for Models 1–4) are assumed to be same. Therefore, though the simpliﬁed mass-spring model is established for the prototype tall building with square cross-section in Section 3.3, it can also be used to calculate the wind-induced responses of other tall buildings. 4. Results analysis 4.1. Along-wind responses Fig. 12 shows the relationship between the extremum tip displacements together with RMS tip accelerations in the along-wind direction and the suction ﬂux coeﬃcient CQ for diﬀerent simpliﬁed mass-spring models. The wind direction angle θ is set as 0°. It can be seen in Fig. 12a that, when there is no air suction (CQ = 0), the reduction of the tip displacement caused by the shape optimization is very signiﬁcant for Model 2 (i.e. the corner-recessed square tall building) and Model 4 (i.e. 93 Engineering Structures 175 (2018) 86–100 45 140 Model 1 Model 2 120 Model 3 Model 4 RMS tip acceleration (mm·s-2) Extremum tip displacement (mm) C. Zheng et al. 100 80 60 40 Model 3 Model 4 35 30 25 20 15 10 20 0.00 (a) Model 1 Model 2 40 0.01 0.02 0.03 0.04 0.00 (b) CQ 0.01 0.02 0.03 0.04 CQ Fig. 12. Along-wind (a) extremum tip displacements and (b) RMS tip accelerations under diﬀerent CQ. the structural frequency, has a narrow bandwidth with large amplitude. It can be seen in Fig. 14a that, the background and resonant components of Model 1 both increase at a low CQ (CQ = 0.0161) and then decrease at a large CQ (CQ = 0.0365), indicating that the suction control can only be eﬀective in reduction of the along-wind response for Model 1 when CQ is large enough. This phenomenon can also be observed in Fig. 12. For the tip displacement spectrum of Model 2 (see Fig. 14b), its magnitude is much less than that of Model 1 for both the background and resonant components, indicating that the eﬀect of shape optimization is very signiﬁcant. Besides, it is clearly illustrated that the background and resonant components are further reduced by the air suction, but the control eﬀect will be not obvious when CQ is larger than 0.0159. The diﬀerent trends of the eﬀect of CQ on the PSD in Fig. 14a and b indicate the mechanism of suction control may be slightly diﬀerent for Model 1 and Model 2, and it can be inferred that the location of the reattachment of separated ﬂows will account for it. Firstly, as the leading edge of the side face for Model 1 is much sharper than that for Model 2, and also the after-body length of Model 1 is relatively larger than that of Model 2, the vortex shedding for the former model will be more signiﬁcant. Secondly, for Model 1, as the suction control can deﬂect the separated ﬂows and promote their reattachment, most of the separated ﬂows will reattach at the recirculation region with a dramatic ﬂuctuation when CQ is small (e.g. CQ equals to 0.0161 in Fig. 14a), and 110 Extremum tip displacement (mm) Extremum tip displacement (mm) except for Model 1, whose extremum tip displacement shows a slight increase as θ increases. Moreover, the combined aerodynamic control can also reduce the extremum tip displacements when θ is less than 30°. After comparison of the tip displacements with and without suction control, it can be clearly identiﬁed that the suction control can sometimes enlarge the displacements at large wind direction angles, e.g. θ equals to 45° for Model 1, and θ equals to 30° for Models 2–3. And the reason can be attributed to that: When it is at large wind direction angle, the suction control will be operated in the leeward face, so the vortices near the face will be regenerated due to the air suction, and also the wake length will be reduced. Therefore, the above reason can result in an increase of the extremum tip displacements for the models. However, the eﬀect of suction control on the tip displacements of Model 4 is diﬀerent from the above analysis, because the suction control has already operated in the leeward face at a small oblique wind direction (θ < 30°). The power spectra density (PSD) for the ﬂuctuating tip displacements of Models 1–2 under diﬀerent CQ are shown in Fig. 14. The wind direction angle is set as 0°. The standard deviation of the tip displacement, which can be calculated by summation of the areas below each curve, can be further divided into the background and resonant components. The background component represents the quasi-static response caused by the gust spectrum with a broad bandwidth; and the resonant component, which is related to the magniﬁed response near 100 (a) 90 80 Model 1 Model 2 Model 3 Model 4 70 60 0 15 30 45 60 (b) θ (°) 120 100 80 60 Model 1 Model 2 Model 3 Model 4 40 20 0 15 30 θ (°) Fig. 13. Along-wind extremum tip displacements at diﬀerent θ: (a) Uc = 0 m/s, and (b) Uc = 9 m/s. 94 45 60 Engineering Structures 175 (2018) 86–100 C. Zheng et al. 3000 8000 CQ= 0 0.0159 0.0356 2000 2 S( f ) (m ·s) 6000 S( f ) (m2·s) CQ= 0 0.0161 0.0365 4000 1000 2000 0 (a) 0 0.01 0.1 f (Hz) 1 0.01 (b) 0.1 f (Hz) 1 Fig. 14. Along-wind tip displacement spectra of (a) Model 1 and (b) Model 2 under diﬀerent CQ. the across-wind direction can also be restrained due to a less circulation to generate the ﬂow separation at the leading edge and a short afterbody length to develop the vortices, resulting in a signiﬁcant reduction of the across-wind displacements. As CQ increases, the extremum displacements decrease dramatically for Model 1 and show a tendency to decrease for Model 2, indicating that a larger CQ can lead to a better control eﬀect on the across-wind responses. However, the above regularity is changed for Models 3–4. As CQ increases, the responses decrease ﬁrst and then increase for Model 3, and it shows no obvious change of the across-wind responses for Model 4. The maximum reduction of the extremum tip displacement reaches 47% for Model 1, and 53% for Models 2–3 and 58% for Model 4. It should be noted that the reduction of the across-wind displacements for Models 2–4 caused by air suction are much less than that for Model 1 (47% when CQ equals to 0.0365), especially for Model 4 with a proportion of only 9% when CQ equals to 0.0135. The above results indicate that the vortex shedding for Models 2–4 has already been substantially restrained by the shape optimization, and hence the reduction of the across-wind displacement generated by air suction will not be very signiﬁcant compared to the baseline model (Model 1). The across-wind RMS tip accelerations in Fig. 15b have the same trend with those of the extremum tip displacements in Fig. 15a. The maximum reduction of RMS acceleration reaches 40% for Model 1 when CQ equals to 0.0365, and 62% for Models 2–3 and 69% for Model 4. will reattach at the side faces with a reduced wake width when CQ is large (e.g. CQ equals to 0.0365 in Fig. 14a). While for Model 2, due to the less signiﬁcant vortex shedding, the reattachment of separated ﬂows at the side faces will be promoted, resulting in a reduction of drag force and corresponding along-wind ﬂuctuating displacement. 4.2. Across-wind responses 120 140 Model 1 Model 2 Model 3 Model 4 RMS tip acceleration (mm·s-2) Extremum tip displacement (mm) Fig. 15 shows the relationship between the extremum tip displacements together with RMS tip accelerations in the across-wind direction and the suction ﬂux coeﬃcient CQ for Models 1–4. The wind direction angle θ is set as 0°. It can be seen in Fig. 15a that, when there is no air suction (CQ = 0), the reductions of the across-wind tip displacements caused by the corner recession (Model 2) and corner-chamfering (Model 2) are both very signiﬁcant, with a proportion of 39%. The above reductions are slightly larger Kwok et al.’s research on the maximum reduction of crosswind tip displacement of the CAARC tall building (30%) caused by chamfered corners [41], which further indicates the experimental and analysis results in the present paper are accurate. The reduction of the tip displacement caused by the Y-shaped geometry (Model 4) is the most signiﬁcant, with a proportion of 49%. Therefore, Model 4 shows the best wind-resistance performance in the across-wind direction; and the reason can be attributed to a signiﬁcant restraint of vortex shedding due to the gradually increased frontal area downstream the side face. While for Models 2–3, the vortex shedding in 120 100 80 60 100 Model 3 Model 4 80 60 40 20 0.00 (a) Model 1 Model 2 0.01 0.02 CQ 0.03 0.04 0.00 (b) 0.01 0.02 CQ Fig. 15. Across-wind (a) extremum tip displacements and (b) RMS tip accelerations under diﬀerent CQ. 95 0.03 0.04 Engineering Structures 175 (2018) 86–100 140 Extremum tip dispalcement (mm) Extremum tip dispalcement (mm) C. Zheng et al. Model 1 Model 2 Model 3 Model 4 120 100 80 60 40 20 (a) 0 15 30 45 60 160 140 100 80 60 40 (b) (°) Model 1 Model 2 Model 3 Model 4 120 0 15 30 45 60 (°) Fig. 16. Across-wind extremum tip displacements at diﬀerent θ: (a) Uc = 0 m/s, and (b) Uc = 9 m/s. CQ on the across-wind ﬂuctuating displacements is not very obvious when CQ is larger than or equal to 0.0159, which is similar to the alongwind ﬂuctuating displacements in Fig. 14b. Based on the above statements, it can be concluded that the reduction of the across-wind extremum displacement and RMS tip acceleration caused by combined aerodynamic control (58% and 69% for Model 4) in the present paper are signiﬁcantly larger than the reduction of the across-wind extremum displacement (41%) and slightly larger than the reduction of the RMS tip acceleration (65%) for a 400 m supertall building caused by using a new combined structural system [42], and are signiﬁcantly larger than those reductions (32% and 54%) for the same building caused by using a 1000 t TMD [42]. And these comparisons further indicate the combined aerodynamic control may be more eﬀective than some other measures (such as the new combined structural system and TMD in [42]) to mitigate the wind-induced responses of tall buildings. The across-wind extremum tip displacements of Models 1–4 at different wind direction angles are shown in Fig. 16. When there is no suction control (see Fig. 16a), the maximum extremum tip displacement of Model 1 shows a sharp decrease as θ increases; while the extremum tip displacements of Models 2–4 increase ﬁrst and then decrease as θ increases, and the maximum value occurs when θ equals to 15° for Models 2–3 and θ equals to 30° for Model 4. Furthermore, reduction of the tip displacements due to the shape optimization is only eﬀective when θ equals to 0°, and among them Model 4 has the best wind-resistance performance. The above results imply that the passive aerodynamic control is sometimes only eﬀective in a limited wind direction angles, when the actual situation slightly deviates from the expected condition, the control eﬀect is often not in the best state or even unfavorable to the structure’s performance [26]. When there is suction control (see Fig. 16b), due to the air suction, the most unfavorable wind direction angles are postponed for Models 1–2 and changed from 30° to 15° for Model 4. Moreover, only the wind direction that θ equals to 0° can be observed to have a considerable improvement of the wind-resistance performance for the models under the combined aerodynamic control. Fig. 17 shows the PSD for the across-wind ﬂuctuating tip displacements of Models 1–2 under diﬀerent CQ. The wind direction angle is set as 0°. It can be illustrated in Fig. 17a that, due to the air suction, the resonant component decreases dramatically and the background component increases slightly for Model 1, and the larger CQ is, the better control eﬀect is. For the displacement spectrum of Model 2 in Fig. 17b, its resonant magnitude is much less than that of Model 1 without suction control, indicating that the combination of the corner recession and air suction is very eﬀective in reduction of the resonant responses. Besides, the resonant component decreases dramatically due to the air suction, but the background component increases a lot. So the eﬀect of 4.3. Torsional responses Eﬀect of CQ on the extremum tip torsional displacements of Models 1–4 are shown in Fig. 18. The wind direction angle θ is set as 0°. It can be seen that, when there is no air suction, the torsional displacements can be considerably reduced by the shape optimization, especially for Model 4; however, when the air suction is added, the torsional displacements of Models 1–3 increase as CQ increases, indicating that the suction control would be unfavorable to the wind-resistance performance in the torsional direction. And the reason can be attributed to the fact that the air suction through the two suction holes, which are far from center of the building (see Fig. 3), will generate a large quantity of unsteady small vortices around the hole, so as to increase the torque moment. The larger the CQ is, the more signiﬁcant the torque moment is. While for Model 4, the inﬂuence of suction control on its torsional response seems to be not obvious. The extremum tip torsional displacement of Model 1 under CQ of 0.0323 is about 1.9 times larger than that of the model without suction control. Although the magnitude of torsional displacement is quite small when compared to the along-wind and across-wind displacements in Figs. 12a and 15a respectively, it still should be careful to utilize the suction control for the buildings with a non-symmetric cross-sectional shape or mass and stiﬀness eccentricity. Fig. 19 presents the extremum tip torsional displacements at different wind direction angles. When there is no suction control (see Fig. 19a), the most unfavorable wind direction angles are 0°, 15°, 15°, 30° for Models 1–4 respectively. And the passive aerodynamic control can signiﬁcantly reduce the tip displacements when θ is less than 45°, especially for Model 4. When the models are controlled by air suction with a suction speed Uc of 9 m/s (see Fig. 19b), the most unfavorable wind direction angles will be shifted to 15°, 0°, 0°, 15° for Models 1–4 respectively. Similarly to Figs. 18 and 19a, Model 4 is the most eﬀective in suppressing the torsional displacement, while the suction control almost has no eﬀect. The PSD for the ﬂuctuating tip torsional displacements of Models 1–2 are shown in Fig. 20. It can be illustrated that, as CQ increases, the background and resonant components both increase for Model 1, while the background component decreases and the resonant component increases for Model 2. The opposite results in the background component for Model 1 and Model 2 may result from the diﬀerent locations of the 96 Engineering Structures 175 (2018) 86–100 C. Zheng et al. 70000 60000 20000 S( f ) (m2·s) S( f ) (m2·s) 50000 C Q= 40000 0 0.0161 0.0365 30000 CQ= 0 0.0159 0.0356 10000 20000 10000 0 0 0.01 (a) 0.1 f (Hz) 1 (b) 0.01 0.1 f (Hz) 1 Torsional extremum tip displacement (rad) Fig. 17. Across-wind tip displacement spectra of (a) Model 1 and (b) Model 2 under diﬀerent CQ. 2.4E-03 Model 1 Model 2 2.0E-03 control on the wind-induced responses of tall buildings, three values, including value 1, value 2, value 3, are deﬁned by Eqs. (11)–(13) to quantitatively express the reduction of the responses caused by the passive aerodynamic control (shape optimization), active aerodynamic control (air suction) and combined aerodynamic control respectively. Model 3 Model 4 1.6E-03 value 1 = r b−rp value 3 = (11) rb 1.2E-03 r b−rp+a 8.0E-04 (12) rb (13) value 2 = value 3−value 1 4.0E-04 where rb represents the wind-induced response of the baseline model (Model 1) without suction control, and rp and rp+a represent the windinduced response of tall buildings controlled by the passive aerodynamic control and combined aerodynamic control respectively. When the value 2 is positive, it means that the suction control can reduce the wind-induced response, and vice versa. The value 1, maximum (when air suction can reduce the wind-induced response) or minimum (when air suction can increase the windinduced response) value 2 and value 3, and the corresponding CQ for Models 1–4 are listed in Table 4 respectively. The wind direction angle is set as 0°, and the response is the extremum tip displacement of tall buildings. It can be seen in Table 4 that, in the along-wind direction, the maximum reduction of the extremum tip displacement caused by the 0.0E+00 0.00 0.01 0.02 CQ 0.03 0.04 Fig. 18. Extremum tip torsional displacement under diﬀerent CQ. separated ﬂows’ reattachment, which is similar to the PSD in Fig. 14. 5. Discussions Extremum tip torsional displacement (rad) Extremum tip torsional displacement (rad) In order to intuitively show the eﬀect of the combined aerodynamic 1.2E-03 Model 1 Model 2 Model 3 Model 4 1.0E-03 8.0E-04 6.0E-04 4.0E-04 2.0E-04 0.0E+00 0 (a) 15 30 (°) 45 60 2.4E-03 Model 1 Model 2 Model 3 Model 4 2.0E-03 1.6E-03 1.2E-03 8.0E-04 4.0E-04 0.0E+00 0 (b) 15 30 (°) Fig. 19. Extremum tip torsional displacement at diﬀerent θ: (a) Uc = 0 m/s, and (b) Uc = 9 m/s. 97 45 60 Engineering Structures 175 (2018) 86–100 C. Zheng et al. 5.0E-06 2.0E-06 0 0.0161 0.0365 3.0E-06 2 S( f ) (rad ·s) S( f ) (rad2·s) C Q= CQ = 4.0E-06 2.0E-06 0 0.0159 0.0356 1.0E-06 1.0E-06 0.0E+00 0.01 0.1 (a) 0.0E+00 0.01 1 f (Hz) 0.1 (b) 1 f (Hz) Fig. 20. Tip torsional displacement spectra of (a) Model 1 and (b) Model 2 under diﬀerent CQ. Table 4 Value 1, value 2, value 3 and corresponding CQ for Models 1–4 under combined aerodynamic control. Model Model Model Model Model Along-wind response 1 2 3 4 Across-wind response Torsional response Value 1, value 2, value 3 CQ Value 1, value 2, value 3 CQ Value 1, value 2, value 3 CQ 0, 0.22, 0.22 0.34, 0.29, 0.63 0.24, 0.27, 0.51 0.30, 0, 0.30 0.0365 0.0159 0.0356 0 0, 0.47, 0.47 0.39, 0.14, 0.53 0.39, 0.13, 0.52 0.49, 0.09, 0.58 0.0365 0.0356 0.0198 0.0135 0, −0.91, −0.91 0.45, −0.30, 0.15 0.49, −0.59, −0.10 0.60, −0.16, 0.44 0.0323 0.0356 0.0323 0.0162 Eqs. (14) and (15) to express the maximum and minimum reduction of the responses caused by the shape optimization and combined aerodynamic control respectively at all the wind direction angles. As the wind-induced responses of the baseline model (Model 1) reach to the maximum values at wind direction angle of 0° (see Figs. 13a, 16a, 19a), the wind-induced response at 0° (rb,θ=0) is adopted as the baseline value in the equations. shape optimization, air suction and combined aerodynamic control are all belonged to Model 2, with a proportion of 34%, 29% and 63% respectively, and the optimal suction ﬂux coeﬃcient CQ is 0.0159. In the across-wind direction, the maximum reduction of the extremum tip displacement caused by the shape optimization and combined aerodynamic control are both belonged to Model 4, with a proportion of 49% and 58% respectively, and the maximum reduction of the displacement caused by air suction belongs to Model 1 with a proportion of 47%. Furthermore, for the tip torsional displacements, it can be illustrated that a signiﬁcant reduction of them is caused by the shape optimization, with a maximum reduction of 60% for Model 4. However, the air suction will increase torsional displacements, and the maximum increase of the torsional displacement occurs at Model 1 with a proportion of 91%. Besides, according to the above statements in Section 4, the eﬀect of combined aerodynamic control on the wind-induced responses will be quite diﬀerent when θ varies. So the value 4 and value 5 are deﬁned by value 4 = r b, θ = 0−min{rθ |θ = 0°, 15°, 30°, 45°, 60°} r b, θ = 0 (14) value 5 = r b, θ = 0−max{rθ |θ = 0°, 15°, 30°, 45°, 60°} r b, θ = 0 (15) where rθ represents the wind-induced response of Models 1–4 at diﬀerent wind direction angles, and rθ can be used to express the wind-induced response of tall buildings controlled by the passive aerodynamic control rp and combined aerodynamic control rp+a respectively. Table 5 Value 4, value 5 and corresponding θ for Models 1–4 with/without suction control. Model Uc = 0 m/s Along-wind response Across-wind response Torsional response Uc = 9 m/s Along-wind response Across-wind response Torsional response Model 1 Model 2 Model 3 Model 4 Value 4 and corresp. θ 0.06, 45° 0.34, 0° 0.24, 0° 0.31, 15° 0.02, 0.59, 0.39, 0.70, 0.23, 0.07, 0.59, 0.41, 0.67, 0.59, 30° 60° 30° 60° 30° 0.22, 0.06, 0.58, 0.28, 0.68, 0.51, 0° 30° 60° 15° 45° 15° Value Value Value Value Value 5 4 5 4 5 and and and and and corresp. corresp. corresp. corresp. corresp. θ θ θ θ θ 0, 0° 0.69, 45° 0, 0° 0.66, 45° 0, 0° 0.08, 0.58, 0.37, 0.61, 0.23, Value Value Value Value Value Value 4 5 4 5 4 5 and and and and and and corresp. corresp. corresp. corresp. corresp. corresp. θ θ θ θ θ θ 0.21, 0° −0.06, 45° 0.63, 45° 0.23, 15° 0.57, 45° −1.15, 15° 0.63, 0° 0, 30° 0.60, 45° −0.10, 30° 0.47, 45° 0.12, 30° 98 30° 30° 15° 45° 15° 45° 45° 15° 45° 15° 0.51, 0° −0.10, 45° 0.52, 45° 0.29, 15° 0.60, 45° −0.06, 0° Engineering Structures 175 (2018) 86–100 C. Zheng et al. Table 5 shows the value 4, value 5 and the corresponding θ for Models 1–4 with suction control (Uc = 9 m/s) and without suction control (Uc = 0 m/s). For Model 1 without air suction, the maximum reduction of the responses (value 4) caused by wind direction angles can reach to 0.06, 0.69 and 0.66 in the along-wind, across-wind and torsional directions respectively, and the most unfavorable wind direction angle is 0°. However, when Model 1 is under air suction (Uc = 9 m/s), its most unfavorable wind direction angle is almost shifted to 15°. For Models 2–3, the most unfavorable wind direction angle is almost shifted from 15° to 30° when the air suction is added, and the maximum reduction of the responses is quite considerable. For Model 4, though the most unfavorable wind direction angle is decreased due to air suction, the reduction of the torsional responses is quite large at all wind direction angles. This paper discusses the inﬂuences of the combined aerodynamic control on wind-induced responses of a tall building with a speciﬁc dynamic property (see Sections 3.3 and 3.4). For the tall buildings with diﬀerent dynamic properties, such as the natural frequency, modal shape, and damping ratio, inﬂuence of the combined aerodynamic control on the wind responses is still an issue for future research, and are not discussed in this paper due to the limited space. unfavorable to the torsional responses. The torsional displacement of Model 1 under CQ of 0.0323 is about 1.9 times larger than that of the model without suction control. However, the maximum reduction of the torsional responses caused by the combined aerodynamic control can still be very considerable at diﬀerent wind direction angles, with a value of 0.57, 0.47, 0.60 and 0.68 for Models 1–4 respectively when Uc equals to 9 m/s. This study contributes to a new aerodynamic control strategy for the designers to look for a solution to the wind-resistance design of tall buildings, especially for a particularly challenging project. Acknowledgement The authors want to express their appreciation for the ﬁnancial support provided by the National Natural Science Foundation of China (Nos. 51578186 and 51108142). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.engstruct.2018.08.031. 6. Conclusions References Characteristics of wind-induced responses of a tall building under the combined aerodynamic control, consisted of the shape optimization of the cross-section (includes the square, corner-recessed square, corner-chamfered square and Y-shaped cross-sections, and are denoted as Models 1–4 respectively) and air suction, are analyzed. 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[24] Chng TL, Rachman A, Tsai HM, Zha GC. Flow control of an airfoil via injection and • For the along-wind responses, the combined aerodynamic control • • exhibits great performance in reduction of the extremum tip displacements at most cases. When the wind direction angle θ is equal to 0°, Model 2 under suction control is the most eﬀective in reducing the along-wind responses, with a reduction of the extremum displacement of 63% (includes 34% caused by shape optimization and 29% caused by air suction) at a relatively low suction ﬂux coeﬃcient (CQ = 0.0159). Besides, for other wind direction angles, the maximum reduction of the along-wind responses is almost less than that for θ is equal to 0°; the most unfavorable wind direction angle is changed due to the air suction, whose function is essentially a dynamic virtual shape. Both the background and resonant components in the PSD for the along-wind responses of Model 2 are signiﬁcantly reduced when CQ equals to 0.0159. The combined aerodynamic control is also very eﬀective in reducing the across-wind responses at most cases. When the wind direction angle θ is equal to 0°, the maximum reduction of the across-wind extremum tip displacements caused by the shape optimization and combined aerodynamic control are both belonged to Model 4, with a proportion of 49% and 58% respectively; and the maximum reduction of the across-wind displacements caused by the air suction occurs at Model 1, with a proportion of 47%. Besides, the resonant component in the PSD for the across-wind responses is signiﬁcantly reduced due to the shape optimization; and as CQ increases, the background component increased slightly and the resonant component decreases dramatically. Though the shape optimization can considerably decrease the torsional extremum tip displacements of the baseline model (Model 1), it should be noted that the air suction will increase the torque moment. 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